Question: Simplify the following expression: $ a = \dfrac{5y - 5}{-4} + \dfrac{9}{2} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{5y - 5}{-4} \times \dfrac{2}{2} = \dfrac{10y - 10}{-8} $ Multiply the second expression by $\dfrac{-4}{-4}$ $ \dfrac{9}{2} \times \dfrac{-4}{-4} = \dfrac{-36}{-8} $ Therefore $ a = \dfrac{10y - 10}{-8} + \dfrac{-36}{-8} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{10y - 10 - 36}{-8} $ $a = \dfrac{10y - 46}{-8}$ Simplify the expression by dividing the numerator and denominator by -2: $a = \dfrac{-5y + 23}{4}$